Square Root of 5/4
2026-02-28 06:01 Diff
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Last updated on August 5, 2025

If a number is multiplied by itself, the result is a square. The inverse of squaring a number is finding its square root. The square root has applications in various fields, such as vehicle design and finance. Here, we will discuss the square root of 5/4.

What is the Square Root of 5/4?

The square root is the inverse operation of squaring a number. The value 5/4 is not a perfect square. The square root of 5/4 can be expressed in both radical and exponential forms. In radical form, it is expressed as √(5/4), whereas in exponential form, it is expressed as (5/4)^(1/2). The square root of 5/4 is approximately 1.11803, which is an irrational number because it cannot be expressed as a fraction of integers.

Finding the Square Root of 5/4

The prime factorization method is typically used for perfect square numbers. However, for non-perfect squares like 5/4, we use methods such as the simplification of fractions, the long-division method, and approximation. Let us now explore these methods:

  • Simplification of fractions
  • Long division method
  • Approximation method

Square Root of 5/4 by Simplification of Fractions

To find the square root of a fraction, we take the square root of the numerator and the denominator separately.

Step 1: The fraction is 5/4.

Step 2: The square root of 5 is √5 and the square root of 4 is √4 = 2.

Step 3: Therefore, the square root of 5/4 is √5/2.

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Square Root of 5/4 by Long Division Method

The long division method is used for finding more precise decimal values of square roots. Here’s how we can find the square root of 5/4 using this method:

Step 1: Convert the fraction 5/4 into a decimal, which is 1.25.

Step 2: Group the numbers from the decimal point. In this case, we start with 1.25.

Step 3: Find a number whose square is less than or equal to the first group (1.25). Here, 1 x 1 = 1 is less than 1.25.

Step 4: Subtract 1 from 1.25 to get 0.25, and bring down two zeros to make it 25.

Step 5: Double the quotient (1) and use it as the new divisor: 2x.

Step 6: Find x such that 2x × x is less than or equal to 25. x is 1, as 21 × 1 = 21.

Step 7: Subtract 21 from 25 to get 4, bring down more zeros, and continue the process to get more decimal places.

The square root of 1.25 is approximately 1.11803.

Square Root of 5/4 by Approximation Method

The approximation method provides a quick way to estimate square roots. Here’s how to find the square root of 5/4 using this method:

Step 1: Identify the perfect squares near 1.25. The perfect squares closest to 1.25 are 1 (1^2) and 1.44 (1.2^2).

Step 2: Since 1.25 is closer to 1.44, start with 1.1 as a rough estimate.

Step 3: Calculate 1.1 × 1.1 = 1.21, which is less than 1.25. Step 4: Increase the estimate slightly to find a closer approximation, resulting in approximately 1.11803.

Common Mistakes and How to Avoid Them in the Square Root of 5/4

Students make common mistakes when finding square roots, such as forgetting about negative square roots and misapplying methods. Let’s explore these mistakes in detail.

Problem 1

Can you help Max find the area of a square with side length √(5/4)?

Okay, lets begin

The area of the square is approximately 1.25 square units.

Explanation

Area of the square = side^2.

The side length is given as √(5/4).

Area of the square = (√(5/4))^2 = 5/4 = 1.25.

Therefore, the area of the square is approximately 1.25 square units.

Well explained 👍

Problem 2

A rectangle has a length of 5 units and a width of √(5/4) units. What is its area?

Okay, lets begin

The area of the rectangle is approximately 5.59015 square units.

Explanation

Area = length × width = 5 × √(5/4).

First, calculate √(5/4) ≈ 1.11803.

Then, area = 5 × 1.11803 = 5.59015 square units.

Well explained 👍

Problem 3

Calculate √(5/4) × 8.

Okay, lets begin

Approximately 8.94424.

Explanation

Find the square root of 5/4, which is approximately 1.11803.

Multiply 1.11803 by 8. 1.11803 × 8 ≈ 8.94424.

Well explained 👍

Problem 4

What will be the square root of (5 + 4)?

Okay, lets begin

The square root is 3.

Explanation

Find the sum of (5 + 4) = 9. Then, √9 = 3. Therefore, the square root of (5 + 4) is ±3.

Well explained 👍

Problem 5

Find the perimeter of a rectangle if its length ‘l’ is 5 units and the width ‘w’ is √(5/4) units.

Okay, lets begin

The perimeter of the rectangle is approximately 12.23606 units.

Explanation

Perimeter of the rectangle = 2 × (length + width). Perimeter = 2 × (5 + √(5/4)) ≈ 2 × (5 + 1.11803) ≈ 2 × 6.11803 ≈ 12.23606 units.

Well explained 👍

FAQ on Square Root of 5/4

1.What is √(5/4) in its simplest form?

The simplest form of √(5/4) is √5/2, which simplifies the square root of the numerator and the denominator separately.

2.Mention the factors of 5/4.

The number 5/4 can be expressed as a fraction of integers, and its factors include 1, 5 (numerator), and 1, 2, and 4 (denominator).

3.Calculate the square of 5/4.

The square of 5/4 is (5/4) × (5/4) = 25/16.

4.Is 5/4 a rational number?

Yes, 5/4 is a rational number because it can be expressed as a fraction of integers.

5.What is the decimal representation of 5/4?

Important Glossaries for the Square Root of 5/4

  • Square root: The square root is the operation that finds a number which, when multiplied by itself, gives the original number. Example: The square root of 4 is 2, as 2 × 2 = 4.
  • Rational number: A rational number can be expressed as a fraction of two integers, where the denominator is not zero.
  • Irrational number: An irrational number cannot be expressed as a simple fraction of two integers. Example: The square root of 2 is irrational.
  • Fraction: A fraction represents a part of a whole and is expressed as a ratio of two numbers, the numerator and the denominator.
  • Decimal: A decimal is a number that has a whole number and a fractional part separated by a decimal point. Example: 1.25 is a decimal.

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Jaskaran Singh Saluja

About the Author

Jaskaran Singh Saluja is a math wizard with nearly three years of experience as a math teacher. His expertise is in algebra, so he can make algebra classes interesting by turning tricky equations into simple puzzles.

Fun Fact

: He loves to play the quiz with kids through algebra to make kids love it.